Cremona's table of elliptic curves

101568 = 2⁶ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	101568by	Isogeny class
Conductor	101568	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3784704	Modular degree for the optimal curve
Δ	-2.6681630004694E+20	Discriminant
Eigenvalues	2- 3+  0 -2  0 -2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6154033,5930455441]	[a1,a2,a3,a4,a6]
Generators	[1365:8464:1]	Generators of the group modulo torsion
j	-10627137250000/110008287	j-invariant
L	3.3393382321934	L(r)(E,1)/r!
Ω	0.17511816314846	Real period
R	2.3836321261786	Regulator
r	1	Rank of the group of rational points
S	0.99999999872098	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	101568p1 25392f1 4416p1	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 101568by1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	0	-2	0	-2	-8	-6	-	-2	4	6	10	-6	0	12	4	-10	6	0	2	-6	0	12	-6

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Quadratic twists for elliptic curve 101568by1

-4	8	-23
101568p1	25392f1	4416p1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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